find the product
(2a+1) cubed
To find the product of the expression (2a + 1) cubed, we can use the binomial expansion formula. According to this formula, the cube of a binomial expression (a + b) can be expanded as follows:
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
In our case, a = 2a and b = 1. Let's substitute these values into the formula:
(2a + 1)^3 = (2a)^3 + 3(2a)^2(1) + 3(2a)(1)^2 + (1)^3
Simplifying this expression further, we have:
(2a + 1)^3 = 8a^3 + 12a^2 + 6a + 1
Therefore, the product of the expression (2a + 1) cubed is 8a^3 + 12a^2 + 6a + 1.